I don't get the idea about the last month's rent. But you can charge the security deposit which is refundable and first month's rent in advance.

 In reality, you have not given enough information, but here goes on a guess...your private property, yes you can charge 1st, last month + security deposit. I see it all the time and have had to pay exactly that.  most of the time , last month rent is to cover your butt should your tenant decide to not pay that last month when they notify you they are moving.i have paid into that situation at a large complex ($2,400 to move in)  $800 rent, $800 last month, and $800 security deposit...i took very good care of my place...that was a lot of money. I also paid that to move into a side-by-side duplex w/garage.  i live in a adjoining state to you. I'm sure you are ok with doing the rent this way, your place...you make the rules !